Only a licensed lawyer can give you legal advice and determining whether you have a viable lawsuit is something only a lawyer can tell you. We can give opinions, however but it is just a general opinion. You have to go through the proper protocol. You were charged with theft. It may have been erroneous but, you cannot just run from it. You have to resolve it. The rental company has acknowledged their error/failure to document the pickup so you should ask them to contact the employer and explain that they made a mistake and are working toward fixing their error with the court. Meanwhile, go to your hearing and show the judge your proof of the pick up. Meanwhile, the rental company should be filing the necessary documentation to get the charges withdrawn. Your responsibility is to responsibly follow up to make sure those things are done, in a calm manner so that they willingly co-operate. If you need to hire a lawyer to make sure the court record is set straight - that the docket shows that it was an error, rather than just being withdrawn, then do it and send the lawyer's bill to the rental company for reimbursement. If they don't pay it, you can sue them but, I highly doubt that would be necessary.
Certified Paralegal, with 25+ years' experience.